Question

Triangle not drawn to scale

Given: m&A=40°,m&B=88°,a=15cm. Then b
= _?__cm to the nearest hundredth

Answer 1

b = 23.3

Explanation:

First, we need to determine whether this is a right or non-right triangle.

We know that the sum of all the angles in a triangle must add up to 180, so we can add angles A and B and subtract the sum from 180:

`180-(40+88)=180-128=52`

The 52 indicates that it is a non-right triangle, so we must rely on either the law of sines or law of cosines to find the measure of b.

Given that we have angle A and its resulting side, a, along with angle B, we can use the law of sines:

`(sin A)/(a)=(sin B)/(b)`

`(sin 40)/(15)=(sin 88)/(b)\\ \\ 15*sin 88=b * sin 40\\\\b=(b*sin 40)/(sin 88)\\ \\b=23.3216=23.3`